June 3 (Reuters) - Australia's APM Human Services International Ltd will be acquired by U.S.-based private equity firm Madison Dearborn Partners in a deal valuing the company's equity at A$1.3 billion ($865.2 million), APM said on Monday. ($1 = 1.5026 Australian dollars) (Reporting by Roushni Nair in Bengaluru; Editing by Jacqueline Wong)